%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN075+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:26:44 PM UTC 2026
% Result : Theorem 3.89s 1.26s
% Output : Refutation 4.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 17 unt; 0 def)
% Number of atoms : 477 ( 25 equ)
% Maximal formula atoms : 23 ( 8 avg)
% Number of connectives : 801 ( 382 ~; 349 |; 70 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 46 ( 15 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 0 con; 1-2 aty)
% Number of variables : 457 ( 402 !; 55 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ r2(X0,X2)
& X2 != X1 )
| ( r2(X0,X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ r3(X0,X1,X3)
& X3 != X2 )
| ( r3(X0,X1,X3)
& X3 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f5,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( ? [X4] :
( r2(X1,X4)
& r3(X0,X4,X3) )
& X3 = X2 )
& ? [X5] :
( r2(X5,X2)
& r3(X0,X1,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
fof(f8,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r3(X0,X2,X1) )
& X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
fof(f9,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r4(X0,X2,X1) )
& ? [X3] :
( r1(X3)
& X1 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).
fof(f12,conjecture,
? [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r2(X6,X5)
& ? [X7] :
( r2(X7,X6)
& ? [X8] :
( r2(X8,X7)
& ? [X9] :
( r2(X9,X8)
& ? [X10] :
( r1(X10)
& r2(X10,X9) ) ) ) ) ) ) ) ) ) )
& ? [X11] :
( ? [X12] :
( r3(X11,X12,X0)
& ? [X13] :
( r2(X13,X12)
& ? [X14] :
( r1(X14)
& r2(X14,X13) ) ) )
& ? [X15] :
( r2(X15,X11)
& ? [X16] :
( r2(X16,X15)
& ? [X17] :
( r2(X17,X16)
& ? [X18] :
( r2(X18,X17)
& ? [X19] :
( r2(X19,X18)
& ? [X20] :
( r2(X20,X19)
& ? [X21] :
( r1(X21)
& r2(X21,X20) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sevenplustwoeqnine) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r2(X6,X5)
& ? [X7] :
( r2(X7,X6)
& ? [X8] :
( r2(X8,X7)
& ? [X9] :
( r2(X9,X8)
& ? [X10] :
( r1(X10)
& r2(X10,X9) ) ) ) ) ) ) ) ) ) )
& ? [X11] :
( ? [X12] :
( r3(X11,X12,X0)
& ? [X13] :
( r2(X13,X12)
& ? [X14] :
( r1(X14)
& r2(X14,X13) ) ) )
& ? [X15] :
( r2(X15,X11)
& ? [X16] :
( r2(X16,X15)
& ? [X17] :
( r2(X17,X16)
& ? [X18] :
( r2(X18,X17)
& ? [X19] :
( r2(X19,X18)
& ? [X20] :
( r2(X20,X19)
& ? [X21] :
( r1(X21)
& r2(X21,X20) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ! [X1] :
( X0 != X1
| ! [X2] :
( ~ r2(X2,X1)
| ! [X3] :
( ~ r2(X3,X2)
| ! [X4] :
( ~ r2(X4,X3)
| ! [X5] :
( ~ r2(X5,X4)
| ! [X6] :
( ~ r2(X6,X5)
| ! [X7] :
( ~ r2(X7,X6)
| ! [X8] :
( ~ r2(X8,X7)
| ! [X9] :
( ~ r2(X9,X8)
| ! [X10] :
( ~ r1(X10)
| ~ r2(X10,X9) ) ) ) ) ) ) ) ) ) )
| ! [X11] :
( ! [X12] :
( ~ r3(X11,X12,X0)
| ! [X13] :
( ~ r2(X13,X12)
| ! [X14] :
( ~ r1(X14)
| ~ r2(X14,X13) ) ) )
| ! [X15] :
( ~ r2(X15,X11)
| ! [X16] :
( ~ r2(X16,X15)
| ! [X17] :
( ~ r2(X17,X16)
| ! [X18] :
( ~ r2(X18,X17)
| ! [X19] :
( ~ r2(X19,X18)
| ! [X20] :
( ~ r2(X20,X19)
| ! [X21] :
( ~ r1(X21)
| ~ r2(X21,X20) ) ) ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
! [X0,X2] :
( ( ~ r2(X0,X2)
& sK1(X0) != X2 )
| ( r2(X0,X2)
& sK1(X0) = X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f2]) ).
fof(f17,plain,
! [X0,X1,X3] :
( ( ~ r3(X0,X1,X3)
& sK2(X0,X1) != X3 )
| ( r3(X0,X1,X3)
& sK2(X0,X1) = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f3]) ).
fof(f19,plain,
! [X0,X1] :
( r2(X1,sK6(X0,X1))
& r3(X0,sK6(X0,X1),sK5(X0,X1))
& sK4(X0,X1) = sK5(X0,X1)
& r2(sK7(X0,X1),sK4(X0,X1))
& r3(X0,X1,sK7(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X2,sK4(X0,X1)),skolemize(X3,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X5,sK7(X0,X1))],[f5]) ).
fof(f21,plain,
! [X0] :
( r1(sK13(X0))
& r3(X0,sK13(X0),sK12(X0))
& sK12(X0) = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0))],[f8]) ).
fof(f22,plain,
! [X0] :
( r1(sK15(X0))
& r4(X0,sK15(X0),sK14(X0))
& r1(sK16(X0))
& sK14(X0) = sK16(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X1,sK14(X0)),skolemize(X2,sK15(X0)),skolemize(X3,sK16(X0))],[f9]) ).
fof(f29,plain,
! [X2,X0] :
( sK1(X0) != X2
| r2(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| sK2(X0,X1) = X3 ),
inference(cnf_transformation,[],[f17]) ).
fof(f40,plain,
! [X0,X1] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f41,plain,
! [X0,X1] : r2(sK7(X0,X1),sK4(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X0,X1] : sK4(X0,X1) = sK5(X0,X1),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0,X1] : r3(X0,sK6(X0,X1),sK5(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X0,X1] : r2(X1,sK6(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f51,plain,
! [X0] : sK12(X0) = X0,
inference(cnf_transformation,[],[f21]) ).
fof(f52,plain,
! [X0] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f53,plain,
! [X0] : r1(sK13(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f55,plain,
! [X0] : r1(sK16(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f63,plain,
! [X2,X21,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X16,X18,X19,X17,X15,X5,X12,X13,X20] :
( X0 != X1
| ~ r2(X2,X1)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r2(X7,X6)
| ~ r2(X8,X7)
| ~ r2(X9,X8)
| ~ r1(X10)
| ~ r2(X10,X9)
| ~ r3(X11,X12,X0)
| ~ r2(X13,X12)
| ~ r1(X14)
| ~ r2(X14,X13)
| ~ r2(X15,X11)
| ~ r2(X16,X15)
| ~ r2(X17,X16)
| ~ r2(X18,X17)
| ~ r2(X19,X18)
| ~ r2(X20,X19)
| ~ r1(X21)
| ~ r2(X21,X20) ),
inference(cnf_transformation,[],[f14]) ).
fof(f64,plain,
! [X0,X1] : r2(sK7(X0,X1),sK5(X0,X1)),
inference(definition_unfolding,[],[f41,f42]) ).
fof(f69,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f29]) ).
fof(f77,plain,
! [X2,X21,X3,X10,X11,X1,X8,X6,X9,X7,X14,X4,X16,X18,X19,X17,X15,X5,X12,X13,X20] :
( ~ r3(X11,X12,X1)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r2(X7,X6)
| ~ r2(X8,X7)
| ~ r2(X9,X8)
| ~ r1(X10)
| ~ r2(X10,X9)
| ~ r2(X2,X1)
| ~ r2(X13,X12)
| ~ r1(X14)
| ~ r2(X14,X13)
| ~ r2(X15,X11)
| ~ r2(X16,X15)
| ~ r2(X17,X16)
| ~ r2(X18,X17)
| ~ r2(X19,X18)
| ~ r2(X20,X19)
| ~ r1(X21)
| ~ r2(X21,X20) ),
inference(equality_resolution,[],[f63]) ).
fof(f78,plain,
! [X0] : r3(X0,sK13(X0),X0),
inference(forward_demodulation,[],[f52,f51]) ).
fof(f82,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X16,X18,X19,X17,X15,X5,X12,X13] :
( ~ r2(X11,sK6(X9,X10))
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r2(X7,X6)
| ~ r1(X8)
| ~ r2(X8,X7)
| ~ r2(X1,sK5(X9,X10))
| ~ r2(X0,X1)
| ~ r1(X12)
| ~ r2(X12,X11)
| ~ r2(X13,X9)
| ~ r2(X14,X13)
| ~ r2(X15,X14)
| ~ r2(X16,X15)
| ~ r2(X17,X16)
| ~ r2(X18,X17)
| ~ r1(X19)
| ~ r2(X19,X18) ),
inference(resolution,[],[f77,f43]) ).
fof(f83,plain,
! [X0] : sK2(X0,sK13(X0)) = X0,
inference(resolution,[],[f34,f78]) ).
fof(f85,plain,
! [X0,X1] : sK2(X0,X1) = sK7(X0,X1),
inference(resolution,[],[f34,f40]) ).
fof(f86,plain,
! [X0,X1] : sK5(X0,X1) = sK2(X0,sK6(X0,X1)),
inference(resolution,[],[f34,f43]) ).
fof(f90,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X16,X18,X17,X15,X5,X12,X13] :
( ~ r2(X8,sK5(X9,X10))
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r1(X7)
| ~ r2(X7,X6)
| ~ r2(X0,X1)
| ~ r2(X1,X8)
| ~ r1(X11)
| ~ r2(X11,X10)
| ~ r2(X12,X9)
| ~ r2(X13,X12)
| ~ r2(X14,X13)
| ~ r2(X15,X14)
| ~ r2(X16,X15)
| ~ r2(X17,X16)
| ~ r1(X18)
| ~ r2(X18,X17) ),
inference(resolution,[],[f82,f44]) ).
fof(f91,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X16,X17,X15,X5,X12,X13] :
( ~ r2(X0,X1)
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r1(X6)
| ~ r2(X6,X5)
| ~ r2(X1,X7)
| ~ r2(X7,sK7(X8,X9))
| ~ r1(X10)
| ~ r2(X10,X9)
| ~ r2(X11,X8)
| ~ r2(X12,X11)
| ~ r2(X13,X12)
| ~ r2(X14,X13)
| ~ r2(X15,X14)
| ~ r2(X16,X15)
| ~ r1(X17)
| ~ r2(X17,X16) ),
inference(resolution,[],[f90,f64]) ).
fof(f92,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X16,X17,X15,X5,X12,X13] :
( ~ r2(X7,sK2(X8,X9))
| ~ r2(X0,X1)
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r1(X6)
| ~ r2(X6,X5)
| ~ r2(X1,X7)
| ~ r1(X10)
| ~ r2(X10,X9)
| ~ r2(X11,X8)
| ~ r2(X12,X11)
| ~ r2(X13,X12)
| ~ r2(X14,X13)
| ~ r2(X15,X14)
| ~ r2(X16,X15)
| ~ r1(X17)
| ~ r2(X17,X16) ),
inference(forward_demodulation,[],[f91,f85]) ).
fof(f93,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X16,X17,X15,X5,X12,X13] :
( ~ r2(X10,sK6(X0,X1))
| ~ r2(X3,X4)
| ~ r2(X5,X3)
| ~ r2(X6,X5)
| ~ r2(X7,X6)
| ~ r2(X8,X7)
| ~ r1(X9)
| ~ r2(X9,X8)
| ~ r2(X4,X2)
| ~ r1(X10)
| ~ r2(X2,sK5(X0,X1))
| ~ r2(X11,X0)
| ~ r2(X12,X11)
| ~ r2(X13,X12)
| ~ r2(X14,X13)
| ~ r2(X15,X14)
| ~ r2(X16,X15)
| ~ r1(X17)
| ~ r2(X17,X16) ),
inference(superposition,[],[f92,f86]) ).
fof(f94,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X16,X15,X5,X12,X13] :
( ~ r2(X7,sK5(X9,X8))
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r1(X6)
| ~ r2(X6,X5)
| ~ r2(X1,X7)
| ~ r1(X8)
| ~ r2(X0,X1)
| ~ r2(X10,X9)
| ~ r2(X11,X10)
| ~ r2(X12,X11)
| ~ r2(X13,X12)
| ~ r2(X14,X13)
| ~ r2(X15,X14)
| ~ r1(X16)
| ~ r2(X16,X15) ),
inference(resolution,[],[f93,f44]) ).
fof(f95,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X15,X5,X12,X13] :
( ~ r2(X0,X1)
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r1(X5)
| ~ r2(X5,X4)
| ~ r2(X6,sK7(X7,X8))
| ~ r1(X8)
| ~ r2(X1,X6)
| ~ r2(X9,X7)
| ~ r2(X10,X9)
| ~ r2(X11,X10)
| ~ r2(X12,X11)
| ~ r2(X13,X12)
| ~ r2(X14,X13)
| ~ r1(X15)
| ~ r2(X15,X14) ),
inference(resolution,[],[f94,f64]) ).
fof(f96,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X15,X5,X12,X13] :
( ~ r2(X6,sK2(X7,X8))
| ~ r2(X0,X1)
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r1(X5)
| ~ r2(X5,X4)
| ~ r1(X8)
| ~ r2(X1,X6)
| ~ r2(X9,X7)
| ~ r2(X10,X9)
| ~ r2(X11,X10)
| ~ r2(X12,X11)
| ~ r2(X13,X12)
| ~ r2(X14,X13)
| ~ r1(X15)
| ~ r2(X15,X14) ),
inference(forward_demodulation,[],[f95,f85]) ).
fof(f101,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X5,X12,X13] :
( ~ r2(X1,X0)
| ~ r2(X2,X3)
| ~ r2(X4,X2)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r1(X7)
| ~ r2(X7,X6)
| ~ r1(sK13(X0))
| ~ r2(X3,X1)
| ~ r2(X8,X0)
| ~ r2(X9,X8)
| ~ r2(X10,X9)
| ~ r2(X11,X10)
| ~ r2(X12,X11)
| ~ r2(X13,X12)
| ~ r1(X14)
| ~ r2(X14,X13) ),
inference(superposition,[],[f96,f83]) ).
fof(f104,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X5,X12,X13] :
( ~ r2(X14,X13)
| ~ r2(X2,X3)
| ~ r2(X4,X2)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r1(X7)
| ~ r2(X7,X6)
| ~ r2(X3,X1)
| ~ r2(X8,X0)
| ~ r2(X9,X8)
| ~ r2(X10,X9)
| ~ r2(X11,X10)
| ~ r2(X12,X11)
| ~ r2(X13,X12)
| ~ r1(X14)
| ~ r2(X1,X0) ),
inference(forward_subsumption_resolution,[],[f101,f53]) ).
fof(f105,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X5,X12,X13] :
( ~ r2(sK6(X13,X14),X12)
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r1(X5)
| ~ r2(X5,X4)
| ~ r2(X1,X6)
| ~ r2(X7,X8)
| ~ r2(X9,X7)
| ~ r2(X10,X9)
| ~ r2(X11,X10)
| ~ r2(X12,X11)
| ~ r2(X0,X1)
| ~ r1(X14)
| ~ r2(X6,X8) ),
inference(resolution,[],[f104,f44]) ).
fof(f115,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5,X12,X13] :
( ~ r2(sK1(sK6(X12,X13)),X11)
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r2(X4,X3)
| ~ r2(X5,X6)
| ~ r2(X7,X8)
| ~ r2(X9,X7)
| ~ r2(X10,X9)
| ~ r2(X11,X10)
| ~ r2(X0,X1)
| ~ r2(X1,X5)
| ~ r1(X13)
| ~ r2(X6,X8) ),
inference(resolution,[],[f105,f69]) ).
fof(f118,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5,X12] :
( ~ r2(sK1(sK1(sK6(X10,X11))),X9)
| ~ r2(X2,X0)
| ~ r1(X3)
| ~ r2(X3,X2)
| ~ r2(X4,X5)
| ~ r2(X6,X7)
| ~ r2(X8,X6)
| ~ r2(X9,X8)
| ~ r2(X0,X1)
| ~ r2(X1,X12)
| ~ r2(X12,X4)
| ~ r1(X11)
| ~ r2(X5,X7) ),
inference(resolution,[],[f115,f69]) ).
fof(f121,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5] :
( ~ r2(sK1(sK1(sK1(sK6(X8,X9)))),X7)
| ~ r1(X2)
| ~ r2(X2,X0)
| ~ r2(X3,X4)
| ~ r2(X5,X6)
| ~ r2(X7,X5)
| ~ r2(X0,X1)
| ~ r2(X1,X10)
| ~ r2(X10,X11)
| ~ r2(X11,X3)
| ~ r1(X9)
| ~ r2(X4,X6) ),
inference(resolution,[],[f118,f69]) ).
fof(f124,plain,
! [X2,X3,X10,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ r2(sK1(sK1(sK1(sK1(sK6(X6,X7))))),X4)
| ~ r2(X0,X1)
| ~ r2(X2,X3)
| ~ r2(X4,X5)
| ~ r1(X0)
| ~ r2(X1,X8)
| ~ r2(X8,X9)
| ~ r2(X9,X10)
| ~ r2(X10,X2)
| ~ r1(X7)
| ~ r2(X3,X5) ),
inference(resolution,[],[f121,f69]) ).
fof(f127,plain,
! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ r2(sK1(sK1(sK1(sK1(sK1(sK6(X4,X5)))))),X6)
| ~ r2(X2,X3)
| ~ r2(X0,X1)
| ~ r1(X0)
| ~ r2(X1,X7)
| ~ r2(X7,X8)
| ~ r2(X8,X9)
| ~ r2(X9,X2)
| ~ r1(X5)
| ~ r2(X3,X6) ),
inference(resolution,[],[f124,f69]) ).
fof(f130,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ r2(X1,sK1(sK1(sK1(sK1(sK1(sK1(sK6(X8,X7))))))))
| ~ r2(X2,X3)
| ~ r1(X2)
| ~ r2(X3,X4)
| ~ r2(X4,X5)
| ~ r2(X5,X6)
| ~ r2(X6,X0)
| ~ r1(X7)
| ~ r2(X0,X1) ),
inference(resolution,[],[f127,f69]) ).
fof(f131,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ r2(X5,sK1(sK1(sK1(sK1(sK1(sK6(X7,X6)))))))
| ~ r1(X0)
| ~ r2(X1,X2)
| ~ r2(X2,X3)
| ~ r2(X3,X4)
| ~ r2(X4,X5)
| ~ r1(X6)
| ~ r2(X0,X1) ),
inference(resolution,[],[f130,f69]) ).
fof(f132,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r2(X4,sK1(sK1(sK1(sK1(sK6(X5,X6))))))
| ~ r2(X1,X2)
| ~ r2(X2,X3)
| ~ r2(X3,X4)
| ~ r1(X0)
| ~ r1(X6)
| ~ r2(X0,X1) ),
inference(resolution,[],[f131,f69]) ).
fof(f133,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2(X2,sK1(sK1(sK1(sK6(X3,X4)))))
| ~ r2(X1,X2)
| ~ r2(X0,X1)
| ~ r1(X5)
| ~ r1(X4)
| ~ r2(X5,X0) ),
inference(resolution,[],[f132,f69]) ).
fof(f134,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2(X0,sK1(sK1(sK6(X1,X2))))
| ~ r2(X3,X0)
| ~ r1(X4)
| ~ r1(X2)
| ~ r2(X4,X3) ),
inference(resolution,[],[f133,f69]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( ~ r2(X0,sK1(sK6(X1,X2)))
| ~ r1(X3)
| ~ r1(X2)
| ~ r2(X3,X0) ),
inference(resolution,[],[f134,f69]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ r2(X0,sK6(X2,X1))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[],[f135,f69]) ).
fof(f137,plain,
! [X0] :
( ~ r1(X0)
| ~ r1(X0) ),
inference(resolution,[],[f136,f44]) ).
fof(f138,plain,
! [X0] : ~ r1(X0),
inference(duplicate_literal_removal,[],[f137]) ).
fof(f142,plain,
$false,
inference(resolution,[],[f138,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN075+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 22:03:17 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.89/1.26 % (4002495)Detected formulas, will run a generic FOF schedule.
% 3.89/1.26 % (4002500)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2282401700:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.89/1.26 % (4002503)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=327136872:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.89/1.26 % (4002506)dis-21_1_sil=8000:lcm=predicate:random_seed=2087272279:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.89/1.26 % (4002505)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=971726665:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.89/1.26 % (4002502)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2176822715:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.89/1.26 % (4002504)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=84465576:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.89/1.26 % (4002501)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2925284347:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.89/1.26 % (4002503)Refutation not found, incomplete strategy
% 3.89/1.26 % (4002503)------------------------------
% 3.89/1.26 % (4002503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.26 % (4002503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.26 % (4002503)CaDiCaL version: 2.1.3
% 3.89/1.26 % (4002503)Termination reason: Refutation not found, incomplete strategy
% 3.89/1.26 % (4002503)Time elapsed: 0.007 s
% 3.89/1.26 % (4002503)Peak memory usage: 88 MB
% 3.89/1.26 % (4002503)Instructions burned: 10 (million)
% 3.89/1.26 % (4002504)Instruction limit reached!
% 3.89/1.26 % (4002504)------------------------------
% 3.89/1.26 % (4002504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.26 % (4002504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.26 % (4002504)CaDiCaL version: 2.1.3
% 3.89/1.26 % (4002504)Termination reason: Instruction limit
% 3.89/1.26 % (4002504)Termination phase: Saturation
% 3.89/1.26 % (4002504)Time elapsed: 0.042 s
% 3.89/1.26 % (4002504)Peak memory usage: 87 MB
% 3.89/1.26 % (4002504)Instructions burned: 121 (million)
% 3.89/1.26 % (4002506)Instruction limit reached!
% 3.89/1.26 % (4002506)------------------------------
% 3.89/1.26 % (4002506)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.26 % (4002506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.26 % (4002506)CaDiCaL version: 2.1.3
% 3.89/1.26 % (4002506)Termination reason: Instruction limit
% 3.89/1.26 % (4002506)Termination phase: Saturation
% 3.89/1.26 % (4002506)Time elapsed: 0.044 s
% 3.89/1.26 % (4002506)Peak memory usage: 87 MB
% 3.89/1.26 % (4002506)Instructions burned: 131 (million)
% 3.89/1.26 % (4002505)Instruction limit reached!
% 3.89/1.26 % (4002505)------------------------------
% 3.89/1.26 % (4002505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.26 % (4002505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.26 % (4002505)CaDiCaL version: 2.1.3
% 3.89/1.26 % (4002505)Termination reason: Instruction limit
% 3.89/1.26 % (4002505)Termination phase: Saturation
% 3.89/1.26 % (4002505)Time elapsed: 0.054 s
% 3.89/1.26 % (4002505)Peak memory usage: 88 MB
% 3.89/1.26 % (4002505)Instructions burned: 142 (million)
% 3.89/1.26 % (4002515)lrs+10_1_sil=32000:urr=on:br=off:random_seed=677014795:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.89/1.26 % (4002514)lrs+10_1_sil=8000:sp=occurrence:random_seed=1870525379:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.89/1.26 % (4002516)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1732866518:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.89/1.26 % (4002503)------------------------------
% 3.89/1.26 % (4002503)------------------------------
% 3.89/1.26 % (4002515)Instruction limit reached!
% 3.89/1.26 % (4002515)------------------------------
% 3.89/1.26 % (4002515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.26 % (4002515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.26 % (4002515)CaDiCaL version: 2.1.3
% 3.89/1.26 % (4002515)Termination reason: Instruction limit
% 3.89/1.26 % (4002515)Termination phase: Saturation
% 3.89/1.26 % (4002515)Time elapsed: 0.076 s
% 3.89/1.26 % (4002515)Peak memory usage: 90 MB
% 3.89/1.26 % (4002515)Instructions burned: 157 (million)
% 3.89/1.26 % (4002514)Instruction limit reached!
% 3.89/1.26 % (4002514)------------------------------
% 3.89/1.26 % (4002514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.26 % (4002514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.26 % (4002514)CaDiCaL version: 2.1.3
% 3.89/1.26 % (4002514)Termination reason: Instruction limit
% 3.89/1.26 % (4002514)Termination phase: Saturation
% 3.89/1.26 % (4002514)Time elapsed: 0.101 s
% 3.89/1.26 % (4002514)Peak memory usage: 88 MB
% 3.89/1.26 % (4002514)Instructions burned: 285 (million)
% 3.89/1.26 % (4002500)First to succeed.
% 3.89/1.26 % (4002500)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4002495"
% 3.89/1.26 % (4002516)Instruction limit reached!
% 3.89/1.26 % (4002516)------------------------------
% 3.89/1.26 % (4002516)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.26 % (4002516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.26 % (4002516)CaDiCaL version: 2.1.3
% 3.89/1.26 % (4002516)Termination reason: Instruction limit
% 3.89/1.26 % (4002516)Termination phase: Saturation
% 3.89/1.26 % (4002516)Time elapsed: 0.124 s
% 3.89/1.26 % (4002516)Peak memory usage: 89 MB
% 3.89/1.26 % (4002516)Instructions burned: 328 (million)
% 3.89/1.26 % (4002520)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=318883496:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 3.89/1.26 % (4002521)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3955893912:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 3.89/1.26 % (4002521)Refutation not found, incomplete strategy
% 3.89/1.26 % (4002521)------------------------------
% 3.89/1.26 % (4002521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.26 % (4002521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.26 % (4002521)CaDiCaL version: 2.1.3
% 3.89/1.26 % (4002521)Termination reason: Refutation not found, incomplete strategy
% 3.89/1.26 % (4002521)Time elapsed: 0.004 s
% 3.89/1.26 % (4002521)Peak memory usage: 88 MB
% 3.89/1.26 % (4002521)Instructions burned: 4 (million)
% 3.89/1.26 % (4002522)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1466374890:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 3.89/1.26 % (4002500)Refutation found. Thanks to Tanya!
% 3.89/1.26 % SZS status Theorem for theBenchmark
% 3.89/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 4.97/1.46 % (4002500)------------------------------
% 4.97/1.46 % (4002500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.97/1.46 % (4002500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.97/1.46 % (4002500)CaDiCaL version: 2.1.3
% 4.97/1.46 % (4002500)Termination reason: Refutation
% 4.97/1.46 % (4002500)Time elapsed: 0.357 s
% 4.97/1.46 % (4002500)Peak memory usage: 129 MB
% 4.97/1.46 % (4002500)Instructions burned: 974 (million)
% 4.97/1.46 % (4002500)------------------------------
% 4.97/1.46 % (4002500)------------------------------
% 4.97/1.46 % (4002495)Success in time 0.647 s
% 4.97/1.46 % Vampire exiting
%------------------------------------------------------------------------------